In this section, we characterize the mismatch hypothesis as it applies to minority graduation rates. To fix ideas, consider the following characterization of the grad- uation production function for one of the UC campuses. Let PjgpAIq denote the graduation rate that campus j can produce for a minority student with an academic preparation index of AI. For simplicity, assume that this production function is linear and increasing in AI, i.e.,
PjgpAIq φ0j φ1jAI (3.1)
for UC campus j, j 1, ..., J, where φ1j ¡ 0.
One could proceed by specifying the admission criteria of campuses in the pres- ence and absence of affirmative action, characterizing the criteria students have for the campuses to which they apply and to which they enroll if admitted and that cam- puses use in its admission decisions and, thus, the matching of students to colleges (or alternative activities).11 For the purposes of assessing the mismatch hypothesis,
it is sufficient to assume that relative to an affirmative action regime, a college un- der an affirmative action ban will place less (or no) weight on the diversity of an incoming student body and more weight on selecting students based on their aca- demic preparation or AI. The mismatch hypothesis asserts that, under affirmative action, minority students are more likely to be matched to higher quality colleges for which they are less well-prepared than their non-minority counterparts. By banning affirmative action, this form of mismatch of minority students will be reduced, i.e., minority students will be “better matched” to colleges on the basis of their academic preparation (AI), and the outcomes of minorities, such as their graduation rates,
11 See Epple, Romano and Sieg (2008) for such an equilibrium model of college admissions under
will improve.12
The validity of this mismatch explanation hinges on whether colleges differ in their graduation production functions and how they differ between high-quality (more se- lective) and lower quality (less selective) colleges. To see this, consider Figure 1, which illustrates two possibilities for the relationship between the production func- tions of a more-selective college, Campus A, and a less-selective one, Campus B. Panel (a) illustrates the case where Campus A has an absolute advantage over Cam- pus B in producing higher graduation rates for students of all levels of academic preparation (AI). At the same time, the way Panel (a) is drawn, the higher qual- ity campus, A, has a comparative advantage at producing higher graduation rates among better prepared students than Campus B. This latter assumption provides a motivation for why better prepared students tend to attend higher quality colleges.
For the predictions of the mismatch hypothesis to hold, one requires a stronger set of differences between the production functions of higher- and lower-quality cam- puses. To see this, consider Panel (b) of Figure 1. As before, Campus A has a comparative advantage in graduating better prepared students. Now, however, Cam- pus A only has an absolute advantage in the production of graduations for better prepared students, i.e., only for AI ¡ AI. And, Campus B now has an absolute advantage in the production of graduations for less-prepared students (AI AI). Now consider what happens to a minority student with academic preparation AI1
who was admitted and attended Campus A under affirmative action but is no longer able to get into Campus A once affirmative action is banned.13 Because it has an
absolute advantage in graduating less prepared students, this student’s likelihood
12 See Dillon and Smith (2009) for reasons why students end up over-matched or under-matched. 13 If students know their academic preparation then they would presumably internalize the fact
that their graduation rates are lower at the more selective campus. However, as discussed in Arcidiacono, Aucejo, Fang, and Spenner (2011), when schools have private information on the probability of success, it is possible for minority students to be made worse off under affirmative action.
(a) Campus A has absolute advantage in graduations over Campus B for all levels of AI
(b) Campus A better than Campus B at graduating better prepared students (AI ¡ AI) but B better than A for less prepared ones (AI AI)
Figure 1: Alternative Relationships between Graduation Production Functions of Higher Quality and Lower Quality Campuses
of graduating from college increases by enrolling in Campus B, as the mismatch hypothesis predicted.14
As the above discussion makes clear, the mismatch hypothesis requires lower- quality (less selective) universities to have an absolute advantage, and not just a comparative advantage, in graduating less academically prepared minority students.
14Campus B having a comparative, but not absolute, advantage over A with respect to graduations
among less prepared students, as in Panel (a) of Figure 1, is not enough to generate the implications of the mismatch hypothesis. To see this, note that if higher quality colleges have an absolute advantage in graduating all students as in Panel (a), then a less prepared minority student with AI1 (AI1 AI) that was admitted to Campus A under affirmative action will experience a lower,
rather than higher, graduation rate after affirmative action is banned and she can no longer attend Campus A.
Below, we estimate campus-specific graduation production functions for each of the UC campuses and assess whether this condition holds across the UC system’s higher and lower ranked campuses.
Before discussing our estimation strategy, several caveats and comments are in order. First, our claims about what is required about the graduation production functions of more and less selective campuses/colleges for the mismatch hypothesis to hold does not characterize how the admission and enrollment processes of students will change after affirmative action bans like Prop 209. As noted in Section 3.2, the number and composition of minority student enrolled at UC campuses changed with Prop 209. Presumably, a complete model of admission and enrollment selection processes would be required to characterize these outcomes. In what follows, we do not specify or estimate an explicit model, but we do develop strategies to correct for selection effects associated with the Prop 209 ban.
Second, it is possible that affirmative action bans also may affect what colleges do with respect to the graduation rates of minority and non-minority students. For example, colleges subject to affirmative action bans may try to improve their tutoring and counseling programs especially at freshman in order to help them get through their first year of collegiate studies in order to reduce the rates of drop-out and improve graduation rates.
There is anecdotal evidence that UC campuses did take actions after Prop 209 to improve student retention rates. For example, UCLA changed the way its in- troductory courses for first year students were organized in the wake of Prop 209 in an attempt to improve the retention of “disadvantaged students.”15 While some
of these efforts were direct responses to the passage of Prop 209, others appear to have been in response to the rising (and continuing) attention to retaining college
15 See “Intercollegiate Forums at UCLA discuss Retention of Minorities,” Daily Bruin, March 2,
enrollees, especially those from disadvantaged groups.16 We note that the efforts
by UC campuses to improve outreach and retention of minority students after Prop 209 could not directly target racial and ethnic groups, which was deemed a violation of ban on the use of race and ethnicity “in the operation of ... public education” (Text of Proposition 209).17 This led to a restructuring of official campus programs
to target disadvantaged, rather than only minority, students based on “academic profiles, personal backgrounds and social and environmental barriers that may affect [a student’s] university experience, retention and graduation.”18 As a result, some
of these retention efforts in response to, or coincident with, Prop 209 may affect the graduation rates of minority and non-minority students.
In the empirical analyses presented below we allow for post-Prop 209 changes in graduation rates at UC campuses, net of changes in selectivity in student en- rollments and campus-specific graduation production functions. We examine the extent to which such changes occurred not just among minorities but also among non-minorities. The latter effects might be expected to the extent that efforts to im- prove retention and graduation rates were not (or could not be) targeted exclusively to minorities. We refer to these effects as the “university response,” although it is really a residual effect since we are not able to directly quantify or characterize the programs that were put in place to improve retentions after the passage of the ban.